Rockfish Historical Harvest Estimates

Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest and releases of rockfish in Alaska waters and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the the shortcomings of the original Howard methods as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure. The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases. As demonstrated below, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 1.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}) \end{equation}\].

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: HR_fitLBR_2bias_hierPcomp_3pH_CLEAN_thru2023_5e+06_7kn_2025-04-11 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9914

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

Figure 12.- Residuals from logbook harvests

SWHS residuals

Figure 13.- Residuals from SWHS harvests.

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 15.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta3_pH 1 1.543024 beta0_pH 2 1.497801 beta1_pH 5 1.405900 beta1_pelagic 2 1.380645

parameter n badRhat_avg tau_beta0_pH 1 1.364643 beta0_pelagic 2 1.272830 beta2_pH 2 1.155588 beta2_pelagic 2 1.136675

Table 2. Summary of unconverged parameters by area

	BSAI	CI	NSEO	PWSI	PWSO	SOKO2SAP	WKMA
beta0_pelagic	0	0	0	1	1	0	0
beta0_pH	0	1	0	0	0	1	0
beta1_pelagic	0	0	0	1	1	0	0
beta1_pH	1	1	0	1	1	1	0
beta2_pelagic	0	0	1	1	0	0	0
beta2_pH	0	1	0	0	0	0	1
beta3_pH	0	1	0	0	0	0	0
tau_beta0_pH	0	1	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.129	0.073	-0.265	-0.132	0.028
mu_bc_H[2]	-0.096	0.045	-0.172	-0.099	0.005
mu_bc_H[3]	-0.433	0.071	-0.564	-0.435	-0.286
mu_bc_H[4]	-0.990	0.191	-1.364	-0.992	-0.615
mu_bc_H[5]	0.954	1.068	-0.161	0.746	3.459
mu_bc_H[6]	-2.154	0.327	-2.810	-2.154	-1.491
mu_bc_H[7]	-0.448	0.110	-0.667	-0.444	-0.236
mu_bc_H[8]	0.249	0.358	-0.339	0.213	1.056
mu_bc_H[9]	-0.293	0.137	-0.559	-0.295	-0.017
mu_bc_H[10]	-0.106	0.069	-0.233	-0.108	0.034
mu_bc_H[11]	-0.125	0.038	-0.198	-0.125	-0.050
mu_bc_H[12]	-0.254	0.106	-0.484	-0.247	-0.060
mu_bc_H[13]	-0.132	0.077	-0.277	-0.133	0.023
mu_bc_H[14]	-0.301	0.098	-0.502	-0.298	-0.115
mu_bc_H[15]	-0.343	0.051	-0.443	-0.343	-0.240
mu_bc_H[16]	-0.266	0.375	-0.903	-0.297	0.574
mu_bc_R[1]	1.348	0.147	1.062	1.347	1.628
mu_bc_R[2]	1.457	0.093	1.273	1.460	1.638
mu_bc_R[3]	1.401	0.145	1.091	1.406	1.670
mu_bc_R[4]	0.907	0.199	0.490	0.917	1.266
mu_bc_R[5]	1.174	0.467	0.262	1.181	2.085
mu_bc_R[6]	-1.601	0.427	-2.455	-1.596	-0.783
mu_bc_R[7]	0.302	0.196	-0.084	0.302	0.697
mu_bc_R[8]	0.557	0.197	0.165	0.561	0.937
mu_bc_R[9]	0.333	0.207	-0.114	0.348	0.702
mu_bc_R[10]	1.297	0.138	1.014	1.300	1.557
mu_bc_R[11]	1.036	0.098	0.846	1.037	1.229
mu_bc_R[12]	0.817	0.203	0.412	0.823	1.202
mu_bc_R[13]	1.024	0.105	0.821	1.022	1.229
mu_bc_R[14]	0.892	0.141	0.613	0.893	1.163
mu_bc_R[15]	0.783	0.112	0.553	0.783	0.993
mu_bc_R[16]	1.092	0.128	0.848	1.091	1.350
tau_pH[1]	5.214	0.456	4.384	5.193	6.185
tau_pH[2]	2.054	0.222	1.655	2.043	2.519
tau_pH[3]	2.014	0.257	1.557	2.003	2.536
beta0_pH[1,1]	0.538	0.177	0.180	0.542	0.870
beta0_pH[2,1]	1.365	0.179	1.013	1.366	1.702
beta0_pH[3,1]	1.422	0.194	0.987	1.434	1.762
beta0_pH[4,1]	1.573	0.209	1.114	1.586	1.946
beta0_pH[5,1]	-0.868	0.285	-1.492	-0.853	-0.369
beta0_pH[6,1]	-0.762	0.586	-2.164	-0.643	-0.103
beta0_pH[7,1]	-0.517	0.561	-1.922	-0.455	0.423
beta0_pH[8,1]	-0.674	0.289	-1.340	-0.638	-0.199
beta0_pH[9,1]	-0.680	0.293	-1.320	-0.653	-0.175
beta0_pH[10,1]	0.227	0.199	-0.187	0.232	0.603
beta0_pH[11,1]	-0.079	0.166	-0.416	-0.076	0.233
beta0_pH[12,1]	0.480	0.189	0.103	0.479	0.842
beta0_pH[13,1]	0.003	0.145	-0.272	0.003	0.286
beta0_pH[14,1]	-0.311	0.167	-0.647	-0.307	-0.005
beta0_pH[15,1]	-0.036	0.182	-0.400	-0.033	0.321
beta0_pH[16,1]	-0.472	0.356	-1.359	-0.407	0.050
beta0_pH[1,2]	2.818	0.166	2.471	2.823	3.124
beta0_pH[2,2]	2.882	0.136	2.607	2.886	3.140
beta0_pH[3,2]	3.129	0.152	2.850	3.123	3.442
beta0_pH[4,2]	2.947	0.128	2.699	2.945	3.199
beta0_pH[5,2]	4.710	1.350	2.995	4.433	8.064
beta0_pH[6,2]	3.108	0.205	2.709	3.105	3.508
beta0_pH[7,2]	1.972	0.174	1.634	1.977	2.313
beta0_pH[8,2]	2.873	0.172	2.539	2.876	3.204
beta0_pH[9,2]	3.430	0.222	2.996	3.431	3.871
beta0_pH[10,2]	3.748	0.198	3.354	3.754	4.126
beta0_pH[11,2]	-4.854	0.304	-5.451	-4.861	-4.256
beta0_pH[12,2]	-4.769	0.394	-5.586	-4.760	-4.044
beta0_pH[13,2]	-4.577	0.402	-5.340	-4.597	-3.762
beta0_pH[14,2]	-5.606	0.489	-6.626	-5.576	-4.728
beta0_pH[15,2]	-4.285	0.337	-4.937	-4.288	-3.613
beta0_pH[16,2]	-4.876	0.390	-5.717	-4.863	-4.163
beta0_pH[1,3]	0.874	1.067	-1.447	0.863	2.174
beta0_pH[2,3]	2.203	0.165	1.890	2.206	2.522
beta0_pH[3,3]	2.526	0.153	2.227	2.529	2.818
beta0_pH[4,3]	2.960	0.168	2.641	2.956	3.283
beta0_pH[5,3]	2.430	1.561	0.225	2.140	6.296
beta0_pH[6,3]	0.882	0.591	-0.502	0.956	1.877
beta0_pH[7,3]	-0.781	0.476	-1.702	-0.767	0.080
beta0_pH[8,3]	0.302	0.201	-0.107	0.301	0.703
beta0_pH[9,3]	-0.800	0.488	-2.036	-0.719	-0.049
beta0_pH[10,3]	0.320	0.473	-0.794	0.394	1.099
beta0_pH[11,3]	-0.156	0.333	-0.812	-0.158	0.494
beta0_pH[12,3]	-0.826	0.358	-1.618	-0.784	-0.224
beta0_pH[13,3]	-0.135	0.316	-0.753	-0.141	0.510
beta0_pH[14,3]	-0.276	0.275	-0.803	-0.284	0.280
beta0_pH[15,3]	-0.690	0.295	-1.295	-0.676	-0.137
beta0_pH[16,3]	-0.386	0.295	-0.987	-0.385	0.187
beta1_pH[1,1]	3.089	0.323	2.509	3.063	3.777
beta1_pH[2,1]	2.160	0.274	1.656	2.148	2.740
beta1_pH[3,1]	1.973	0.306	1.436	1.953	2.645
beta1_pH[4,1]	2.377	0.327	1.832	2.343	3.085
beta1_pH[5,1]	2.305	0.359	1.752	2.265	3.136
beta1_pH[6,1]	3.900	1.219	2.347	3.605	6.851
beta1_pH[7,1]	2.714	1.111	0.960	2.571	5.473
beta1_pH[8,1]	4.041	0.982	2.638	3.856	6.374
beta1_pH[9,1]	2.374	0.397	1.729	2.336	3.240
beta1_pH[10,1]	2.408	0.281	1.895	2.398	2.987
beta1_pH[11,1]	3.257	0.210	2.855	3.251	3.687
beta1_pH[12,1]	2.554	0.221	2.130	2.548	2.998
beta1_pH[13,1]	2.972	0.217	2.559	2.961	3.403
beta1_pH[14,1]	3.411	0.222	2.989	3.405	3.862
beta1_pH[15,1]	2.543	0.226	2.110	2.541	2.988
beta1_pH[16,1]	4.108	0.648	3.195	3.986	5.685
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.001	0.024	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.002	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.702	0.336	6.061	6.704	7.361
beta1_pH[12,2]	6.441	0.457	5.608	6.426	7.428
beta1_pH[13,2]	6.957	0.444	6.104	6.963	7.826
beta1_pH[14,2]	7.256	0.508	6.336	7.242	8.313
beta1_pH[15,2]	6.764	0.366	6.039	6.760	7.495
beta1_pH[16,2]	7.470	0.428	6.655	7.453	8.345
beta1_pH[1,3]	2.309	2.367	0.000	2.361	7.553
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	9.664	55.642	0.774	2.731	26.618
beta1_pH[6,3]	3.894	12.888	0.456	2.410	10.905
beta1_pH[7,3]	1.881	0.662	0.826	1.825	3.253
beta1_pH[8,3]	2.732	0.389	1.988	2.730	3.501
beta1_pH[9,3]	2.937	0.583	2.016	2.839	4.405
beta1_pH[10,3]	3.058	0.565	2.146	2.983	4.360
beta1_pH[11,3]	2.730	0.396	1.980	2.720	3.506
beta1_pH[12,3]	4.064	0.456	3.221	4.038	5.024
beta1_pH[13,3]	1.716	0.345	1.017	1.726	2.371
beta1_pH[14,3]	2.505	0.354	1.824	2.504	3.203
beta1_pH[15,3]	1.979	0.324	1.363	1.979	2.614
beta1_pH[16,3]	1.788	0.328	1.153	1.782	2.459
beta2_pH[1,1]	0.477	0.119	0.291	0.460	0.761
beta2_pH[2,1]	0.572	0.302	0.253	0.516	1.221
beta2_pH[3,1]	0.638	0.402	0.228	0.556	1.637
beta2_pH[4,1]	0.477	0.182	0.225	0.447	0.897
beta2_pH[5,1]	1.480	0.971	0.243	1.355	3.737
beta2_pH[6,1]	0.184	0.068	0.084	0.175	0.334
beta2_pH[7,1]	0.011	0.060	0.000	0.000	0.086
beta2_pH[8,1]	0.242	0.093	0.124	0.224	0.456
beta2_pH[9,1]	0.421	0.216	0.172	0.383	0.885
beta2_pH[10,1]	0.603	0.256	0.284	0.554	1.239
beta2_pH[11,1]	0.790	0.210	0.467	0.757	1.307
beta2_pH[12,1]	1.330	0.465	0.742	1.238	2.445
beta2_pH[13,1]	0.737	0.216	0.413	0.708	1.247
beta2_pH[14,1]	0.840	0.203	0.535	0.810	1.329
beta2_pH[15,1]	0.797	0.280	0.411	0.751	1.461
beta2_pH[16,1]	0.379	0.168	0.172	0.335	0.795
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-2.036	1.833	-6.761	-1.577	-0.029
beta2_pH[4,2]	-2.052	1.895	-7.016	-1.561	-0.033
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.368	4.327	-20.588	-8.261	-3.981
beta2_pH[12,2]	-7.804	5.072	-20.940	-6.817	-0.964
beta2_pH[13,2]	-7.649	4.942	-19.886	-6.557	-1.658
beta2_pH[14,2]	-8.347	4.636	-20.245	-7.209	-2.495
beta2_pH[15,2]	-9.142	4.371	-20.515	-8.013	-3.805
beta2_pH[16,2]	-9.283	4.273	-20.395	-8.205	-3.982
beta2_pH[1,3]	0.221	0.528	0.000	0.138	0.989
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	5.437	5.666	-1.219	3.779	20.133
beta2_pH[6,3]	5.578	5.619	-0.008	3.816	20.057
beta2_pH[7,3]	4.370	5.797	0.144	1.181	20.513
beta2_pH[8,3]	6.905	5.193	0.791	5.735	20.418
beta2_pH[9,3]	5.515	5.524	0.369	3.771	20.171
beta2_pH[10,3]	5.058	5.554	0.394	2.703	19.905
beta2_pH[11,3]	-2.573	2.513	-9.628	-1.791	-0.569
beta2_pH[12,3]	-2.701	2.395	-9.587	-1.949	-0.925
beta2_pH[13,3]	-3.154	2.731	-10.802	-2.218	-0.773
beta2_pH[14,3]	-3.090	2.636	-10.443	-2.199	-0.876
beta2_pH[15,3]	-3.278	2.733	-11.276	-2.319	-0.965
beta2_pH[16,3]	-3.302	2.788	-11.774	-2.350	-0.872
beta3_pH[1,1]	35.930	0.820	34.400	35.901	37.614
beta3_pH[2,1]	33.560	1.161	31.483	33.473	36.188
beta3_pH[3,1]	33.640	1.051	31.515	33.634	35.782
beta3_pH[4,1]	33.827	1.208	31.646	33.756	36.387
beta3_pH[5,1]	27.709	1.143	26.495	27.459	30.967
beta3_pH[6,1]	38.183	3.217	32.095	38.077	44.695
beta3_pH[7,1]	30.824	7.941	18.531	30.404	45.067
beta3_pH[8,1]	39.985	2.094	36.323	39.740	44.850
beta3_pH[9,1]	30.646	1.522	27.960	30.548	33.900
beta3_pH[10,1]	32.734	0.943	31.000	32.688	34.694
beta3_pH[11,1]	30.356	0.471	29.428	30.358	31.246
beta3_pH[12,1]	30.148	0.401	29.349	30.157	30.908
beta3_pH[13,1]	33.173	0.591	32.066	33.150	34.436
beta3_pH[14,1]	32.030	0.455	31.150	32.024	32.918
beta3_pH[15,1]	31.168	0.644	29.907	31.168	32.445
beta3_pH[16,1]	32.042	1.032	30.395	31.894	34.496
beta3_pH[1,2]	29.919	7.919	18.444	28.920	44.919
beta3_pH[2,2]	29.879	8.015	18.436	28.932	44.957
beta3_pH[3,2]	30.045	8.122	18.411	28.919	45.089
beta3_pH[4,2]	30.161	7.909	18.417	29.247	44.657
beta3_pH[5,2]	30.151	8.008	18.422	29.313	44.945
beta3_pH[6,2]	29.912	7.948	18.405	29.280	44.814
beta3_pH[7,2]	29.986	7.955	18.464	28.861	45.055
beta3_pH[8,2]	30.238	7.936	18.570	29.366	44.863
beta3_pH[9,2]	29.781	8.077	18.448	28.640	45.062
beta3_pH[10,2]	29.654	7.913	18.496	28.475	44.832
beta3_pH[11,2]	43.403	0.178	43.116	43.383	43.781
beta3_pH[12,2]	43.179	0.189	42.877	43.138	43.678
beta3_pH[13,2]	43.868	0.142	43.483	43.907	44.042
beta3_pH[14,2]	43.302	0.201	43.048	43.249	43.812
beta3_pH[15,2]	43.408	0.189	43.112	43.386	43.808
beta3_pH[16,2]	43.498	0.187	43.160	43.501	43.841
beta3_pH[1,3]	35.350	7.082	19.094	37.592	45.111
beta3_pH[2,3]	30.007	7.883	18.441	29.137	44.793
beta3_pH[3,3]	30.226	8.035	18.406	29.461	44.974
beta3_pH[4,3]	30.132	7.815	18.569	29.370	44.935
beta3_pH[5,3]	37.017	4.046	31.234	36.488	45.176
beta3_pH[6,3]	39.705	4.036	31.439	40.318	45.545
beta3_pH[7,3]	32.304	1.530	31.023	31.985	36.062
beta3_pH[8,3]	41.484	0.366	40.790	41.486	42.128
beta3_pH[9,3]	33.216	0.807	31.190	33.421	34.302
beta3_pH[10,3]	35.515	0.991	33.110	35.837	36.850
beta3_pH[11,3]	41.822	0.849	40.083	41.877	43.319
beta3_pH[12,3]	41.725	0.400	40.975	41.733	42.551
beta3_pH[13,3]	42.744	0.932	40.920	42.737	44.883
beta3_pH[14,3]	41.099	0.597	39.831	41.126	42.212
beta3_pH[15,3]	42.636	0.693	41.116	42.720	43.793
beta3_pH[16,3]	42.893	0.761	41.155	43.009	44.140
beta0_pelagic[1]	2.212	0.134	1.957	2.211	2.475
beta0_pelagic[2]	1.516	0.129	1.259	1.519	1.773
beta0_pelagic[3]	-0.571	0.993	-3.337	-0.271	0.553
beta0_pelagic[4]	-0.488	0.957	-2.802	-0.260	0.830
beta0_pelagic[5]	1.190	0.255	0.684	1.190	1.704
beta0_pelagic[6]	1.474	0.270	0.910	1.492	1.972
beta0_pelagic[7]	1.660	0.226	1.257	1.639	2.152
beta0_pelagic[8]	1.765	0.208	1.375	1.761	2.213
beta0_pelagic[9]	2.501	0.311	1.882	2.509	3.080
beta0_pelagic[10]	2.540	0.200	2.136	2.546	2.935
beta0_pelagic[11]	0.152	0.457	-0.898	0.302	0.731
beta0_pelagic[12]	1.676	0.148	1.387	1.676	1.976
beta0_pelagic[13]	0.316	0.192	-0.101	0.329	0.654
beta0_pelagic[14]	-0.089	0.285	-0.715	-0.065	0.394
beta0_pelagic[15]	-0.261	0.143	-0.543	-0.258	0.012
beta0_pelagic[16]	0.333	0.249	-0.322	0.380	0.688
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	2.301	1.803	0.518	1.716	7.583
beta1_pelagic[4]	2.048	1.406	0.378	1.645	6.076
beta1_pelagic[5]	-0.077	0.315	-0.690	-0.080	0.551
beta1_pelagic[6]	-0.104	0.445	-0.847	-0.154	0.733
beta1_pelagic[7]	-0.019	0.322	-0.617	-0.017	0.620
beta1_pelagic[8]	-0.012	0.286	-0.580	-0.011	0.560
beta1_pelagic[9]	0.187	0.486	-0.757	0.278	0.947
beta1_pelagic[10]	0.066	0.260	-0.454	0.066	0.580
beta1_pelagic[11]	3.366	1.027	2.094	3.036	5.785
beta1_pelagic[12]	2.766	0.311	2.198	2.754	3.400
beta1_pelagic[13]	2.870	0.701	1.751	2.795	4.503
beta1_pelagic[14]	4.219	1.004	2.750	4.024	6.480
beta1_pelagic[15]	2.902	0.259	2.389	2.904	3.424
beta1_pelagic[16]	3.456	0.762	2.666	3.256	5.801
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.830	3.502	0.024	0.143	7.348
beta2_pelagic[4]	1.683	5.227	0.023	0.325	16.001
beta2_pelagic[5]	-0.003	0.685	-1.431	-0.005	1.418
beta2_pelagic[6]	-0.103	0.702	-1.533	-0.148	1.446
beta2_pelagic[7]	-0.006	0.665	-1.396	0.003	1.347
beta2_pelagic[8]	-0.004	0.652	-1.428	0.004	1.364
beta2_pelagic[9]	0.170	0.669	-1.266	0.246	1.416
beta2_pelagic[10]	0.050	0.632	-1.426	0.041	1.373
beta2_pelagic[11]	2.751	4.794	0.122	0.427	16.635
beta2_pelagic[12]	6.774	5.318	1.147	5.063	20.642
beta2_pelagic[13]	1.062	2.396	0.198	0.481	6.659
beta2_pelagic[14]	0.356	0.474	0.160	0.300	0.821
beta2_pelagic[15]	6.819	5.238	1.326	5.283	21.201
beta2_pelagic[16]	5.555	5.663	0.213	4.207	21.020
beta3_pelagic[1]	29.671	7.862	18.453	28.646	44.808
beta3_pelagic[2]	29.856	7.916	18.438	28.902	44.848
beta3_pelagic[3]	29.810	6.395	19.111	29.204	43.450
beta3_pelagic[4]	25.520	5.814	18.532	24.194	42.526
beta3_pelagic[5]	30.159	8.282	18.422	28.759	45.213
beta3_pelagic[6]	31.717	6.731	19.038	31.667	44.224
beta3_pelagic[7]	29.256	7.585	18.430	28.295	44.648
beta3_pelagic[8]	29.398	8.029	18.442	27.891	45.034
beta3_pelagic[9]	30.851	6.239	19.114	30.939	43.296
beta3_pelagic[10]	29.526	8.090	18.402	28.194	44.856
beta3_pelagic[11]	42.355	1.987	37.013	43.029	45.405
beta3_pelagic[12]	43.457	0.273	42.993	43.439	43.958
beta3_pelagic[13]	42.775	1.266	40.271	42.756	45.389
beta3_pelagic[14]	42.235	1.616	38.827	42.249	45.362
beta3_pelagic[15]	43.186	0.260	42.549	43.184	43.663
beta3_pelagic[16]	43.145	0.654	41.462	43.218	44.364
mu_beta0_pelagic[1]	0.606	1.103	-1.830	0.692	2.656
mu_beta0_pelagic[2]	1.830	0.396	1.081	1.840	2.589
mu_beta0_pelagic[3]	0.349	0.471	-0.633	0.356	1.276
tau_beta0_pelagic[1]	0.454	0.530	0.047	0.271	1.980
tau_beta0_pelagic[2]	2.739	3.458	0.267	1.977	9.227
tau_beta0_pelagic[3]	1.588	1.223	0.169	1.279	4.664
beta0_yellow[1]	-0.532	0.188	-0.958	-0.518	-0.211
beta0_yellow[2]	0.502	0.168	0.155	0.512	0.793
beta0_yellow[3]	-0.325	0.198	-0.736	-0.313	0.011
beta0_yellow[4]	0.843	0.278	0.075	0.890	1.210
beta0_yellow[5]	-0.300	0.353	-1.003	-0.293	0.397
beta0_yellow[6]	1.118	0.165	0.792	1.119	1.439
beta0_yellow[7]	1.024	0.157	0.722	1.023	1.327
beta0_yellow[8]	1.014	0.157	0.708	1.011	1.322
beta0_yellow[9]	0.672	0.158	0.365	0.669	0.986
beta0_yellow[10]	0.583	0.137	0.325	0.583	0.848
beta0_yellow[11]	-2.013	0.453	-2.909	-1.999	-1.157
beta0_yellow[12]	-3.697	0.421	-4.574	-3.677	-2.907
beta0_yellow[13]	-3.716	0.465	-4.680	-3.684	-2.883
beta0_yellow[14]	-2.160	0.532	-3.092	-2.179	-0.992
beta0_yellow[15]	-2.854	0.428	-3.758	-2.839	-2.041
beta0_yellow[16]	-2.449	0.463	-3.362	-2.454	-1.542
beta1_yellow[1]	0.853	1.104	0.013	0.683	2.792
beta1_yellow[2]	1.067	0.372	0.591	1.020	1.921
beta1_yellow[3]	0.726	0.300	0.266	0.710	1.347
beta1_yellow[4]	1.359	0.722	0.648	1.169	3.542
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.162	0.456	1.301	2.150	3.097
beta1_yellow[12]	2.496	0.436	1.717	2.470	3.434
beta1_yellow[13]	2.834	0.459	2.030	2.802	3.813
beta1_yellow[14]	2.241	0.517	1.114	2.253	3.187
beta1_yellow[15]	2.107	0.426	1.304	2.095	3.001
beta1_yellow[16]	2.208	0.462	1.281	2.209	3.091
beta2_yellow[1]	-3.779	3.091	-11.333	-3.019	-0.081
beta2_yellow[2]	-3.646	3.084	-11.313	-2.808	-0.205
beta2_yellow[3]	-3.537	3.007	-10.860	-2.733	-0.154
beta2_yellow[4]	-3.298	3.243	-11.423	-2.268	-0.106
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.594	2.748	-11.484	-3.944	-1.132
beta2_yellow[12]	-4.877	2.662	-11.535	-4.305	-1.359
beta2_yellow[13]	-4.800	2.551	-11.166	-4.221	-1.589
beta2_yellow[14]	-4.791	2.884	-11.941	-4.208	-0.399
beta2_yellow[15]	-4.441	2.780	-11.580	-3.770	-1.032
beta2_yellow[16]	-5.046	2.865	-12.200	-4.441	-1.328
beta3_yellow[1]	25.472	6.905	18.238	22.542	43.874
beta3_yellow[2]	29.099	1.838	25.868	28.875	32.787
beta3_yellow[3]	32.972	3.123	25.115	32.909	39.283
beta3_yellow[4]	28.968	3.456	22.174	27.958	35.985
beta3_yellow[5]	29.981	7.860	18.479	29.025	44.889
beta3_yellow[6]	29.995	7.876	18.523	29.087	44.757
beta3_yellow[7]	30.433	7.996	18.531	29.649	45.082
beta3_yellow[8]	30.214	8.029	18.440	29.317	45.073
beta3_yellow[9]	30.028	7.891	18.537	28.939	44.900
beta3_yellow[10]	29.799	7.825	18.428	28.595	44.666
beta3_yellow[11]	45.321	0.513	44.091	45.407	45.969
beta3_yellow[12]	43.290	0.399	42.454	43.264	44.063
beta3_yellow[13]	44.869	0.393	44.009	44.946	45.524
beta3_yellow[14]	44.086	1.540	40.613	44.209	45.837
beta3_yellow[15]	45.156	0.518	44.134	45.136	45.966
beta3_yellow[16]	44.567	0.722	43.391	44.569	45.852
mu_beta0_yellow[1]	0.090	0.546	-1.056	0.102	1.214
mu_beta0_yellow[2]	0.653	0.334	-0.022	0.673	1.284
mu_beta0_yellow[3]	-2.487	0.611	-3.477	-2.564	-1.049
tau_beta0_yellow[1]	1.789	2.416	0.102	1.117	6.994
tau_beta0_yellow[2]	3.388	3.949	0.277	2.346	12.371
tau_beta0_yellow[3]	1.484	1.788	0.101	0.984	5.530
beta0_black[1]	-0.068	0.161	-0.372	-0.070	0.266
beta0_black[2]	1.918	0.128	1.670	1.919	2.167
beta0_black[3]	1.320	0.133	1.059	1.320	1.583
beta0_black[4]	2.430	0.134	2.173	2.427	2.699
beta0_black[5]	1.603	1.950	-3.203	1.684	5.601
beta0_black[6]	1.586	1.979	-3.024	1.668	5.622
beta0_black[7]	1.553	2.018	-3.196	1.658	5.527
beta0_black[8]	1.301	0.229	0.852	1.300	1.752
beta0_black[9]	2.449	0.253	1.956	2.443	2.954
beta0_black[10]	1.481	0.132	1.213	1.480	1.739
beta0_black[11]	3.490	0.155	3.181	3.493	3.791
beta0_black[12]	4.873	0.176	4.524	4.875	5.211
beta0_black[13]	-0.158	0.297	-0.750	-0.134	0.321
beta0_black[14]	2.859	0.159	2.546	2.861	3.164
beta0_black[15]	1.285	0.155	0.976	1.287	1.582
beta0_black[16]	4.273	0.159	3.956	4.275	4.579
beta2_black[1]	7.857	9.864	0.549	3.729	38.831
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-1.793	1.575	-6.326	-1.273	-0.220
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.791	1.071	39.881	41.941	43.236
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	38.959	1.802	35.628	39.257	40.526
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.270	0.196	-0.662	-0.267	0.120
beta4_black[2]	0.244	0.183	-0.118	0.247	0.611
beta4_black[3]	-0.936	0.192	-1.306	-0.933	-0.551
beta4_black[4]	0.425	0.220	-0.021	0.421	0.861
beta4_black[5]	0.197	2.503	-4.597	0.132	5.244
beta4_black[6]	0.173	2.349	-4.713	0.114	4.789
beta4_black[7]	0.240	2.400	-4.480	0.188	5.302
beta4_black[8]	-0.702	0.374	-1.462	-0.697	0.040
beta4_black[9]	1.491	1.048	-0.134	1.363	3.907
beta4_black[10]	0.017	0.189	-0.346	0.016	0.388
beta4_black[11]	-0.696	0.213	-1.116	-0.697	-0.273
beta4_black[12]	0.166	0.324	-0.437	0.154	0.824
beta4_black[13]	-1.183	0.227	-1.631	-1.178	-0.743
beta4_black[14]	-0.184	0.236	-0.646	-0.181	0.283
beta4_black[15]	-0.877	0.214	-1.286	-0.874	-0.446
beta4_black[16]	-0.593	0.234	-1.031	-0.599	-0.120
mu_beta0_black[1]	1.289	0.901	-0.608	1.314	3.125
mu_beta0_black[2]	1.576	0.918	-0.747	1.656	3.313
mu_beta0_black[3]	2.486	0.968	0.461	2.524	4.314
tau_beta0_black[1]	0.628	0.586	0.058	0.450	2.178
tau_beta0_black[2]	1.891	3.601	0.054	0.839	10.247
tau_beta0_black[3]	0.234	0.156	0.049	0.194	0.647
beta0_dsr[11]	-2.885	0.284	-3.438	-2.889	-2.327
beta0_dsr[12]	4.557	0.278	4.028	4.551	5.125
beta0_dsr[13]	-1.377	0.384	-2.082	-1.357	-0.771
beta0_dsr[14]	-3.649	0.511	-4.675	-3.653	-2.669
beta0_dsr[15]	-1.940	0.283	-2.506	-1.945	-1.389
beta0_dsr[16]	-2.979	0.362	-3.713	-2.972	-2.287
beta1_dsr[11]	4.820	0.304	4.212	4.821	5.412
beta1_dsr[12]	10.681	58.579	2.188	5.036	22.954
beta1_dsr[13]	2.899	0.470	2.249	2.862	3.666
beta1_dsr[14]	6.312	0.536	5.259	6.313	7.361
beta1_dsr[15]	3.336	0.288	2.767	3.336	3.885
beta1_dsr[16]	5.793	0.378	5.090	5.788	6.550
beta2_dsr[11]	-8.271	2.386	-13.914	-7.927	-4.615
beta2_dsr[12]	-7.109	2.621	-12.997	-6.974	-2.494
beta2_dsr[13]	-6.334	2.820	-12.335	-6.258	-0.560
beta2_dsr[14]	-6.161	2.741	-12.209	-6.060	-1.768
beta2_dsr[15]	-7.763	2.405	-13.180	-7.522	-3.777
beta2_dsr[16]	-7.921	2.319	-13.364	-7.579	-4.350
beta3_dsr[11]	43.484	0.151	43.203	43.485	43.768
beta3_dsr[12]	33.929	0.725	32.007	34.103	34.798
beta3_dsr[13]	43.258	0.393	42.772	43.202	43.889
beta3_dsr[14]	43.353	0.243	43.070	43.280	43.976
beta3_dsr[15]	43.510	0.189	43.161	43.510	43.850
beta3_dsr[16]	43.444	0.160	43.167	43.435	43.766
beta4_dsr[11]	0.587	0.225	0.154	0.584	1.031
beta4_dsr[12]	0.249	0.447	-0.668	0.250	1.141
beta4_dsr[13]	-0.159	0.221	-0.600	-0.153	0.272
beta4_dsr[14]	0.156	0.254	-0.345	0.158	0.644
beta4_dsr[15]	0.721	0.218	0.303	0.719	1.161
beta4_dsr[16]	0.154	0.227	-0.297	0.155	0.608
beta0_slope[11]	-1.846	0.146	-2.129	-1.846	-1.551
beta0_slope[12]	-4.474	0.253	-4.989	-4.467	-4.004
beta0_slope[13]	-1.353	0.194	-1.812	-1.339	-1.032
beta0_slope[14]	-2.672	0.166	-3.003	-2.671	-2.343
beta0_slope[15]	-1.343	0.141	-1.619	-1.346	-1.072
beta0_slope[16]	-2.737	0.154	-3.045	-2.734	-2.445
beta1_slope[11]	4.484	0.217	4.042	4.491	4.902
beta1_slope[12]	3.993	0.446	3.147	3.989	4.874
beta1_slope[13]	2.752	0.521	2.185	2.656	4.493
beta1_slope[14]	6.331	0.418	5.515	6.323	7.165
beta1_slope[15]	3.007	0.208	2.606	3.010	3.413
beta1_slope[16]	5.284	0.282	4.726	5.281	5.854
beta2_slope[11]	8.629	2.335	5.057	8.222	14.025
beta2_slope[12]	6.679	2.932	1.178	6.638	12.563
beta2_slope[13]	5.273	3.076	0.338	5.240	11.516
beta2_slope[14]	6.355	2.510	2.387	6.143	11.835
beta2_slope[15]	8.118	2.305	4.467	7.776	13.442
beta2_slope[16]	7.753	2.248	4.216	7.388	12.999
beta3_slope[11]	43.457	0.134	43.213	43.453	43.721
beta3_slope[12]	43.360	0.278	42.907	43.318	43.952
beta3_slope[13]	43.466	0.404	42.924	43.401	44.263
beta3_slope[14]	43.268	0.136	43.096	43.233	43.614
beta3_slope[15]	43.493	0.163	43.196	43.493	43.799
beta3_slope[16]	43.373	0.141	43.149	43.354	43.689
beta4_slope[11]	-0.732	0.166	-1.051	-0.730	-0.415
beta4_slope[12]	-1.157	0.462	-2.168	-1.130	-0.357
beta4_slope[13]	0.088	0.163	-0.227	0.088	0.410
beta4_slope[14]	-0.095	0.199	-0.483	-0.095	0.299
beta4_slope[15]	-0.767	0.160	-1.090	-0.767	-0.448
beta4_slope[16]	-0.160	0.176	-0.510	-0.161	0.187
sigma_H[1]	0.199	0.056	0.097	0.197	0.315
sigma_H[2]	0.171	0.030	0.118	0.169	0.236
sigma_H[3]	0.196	0.043	0.123	0.193	0.286
sigma_H[4]	0.420	0.077	0.294	0.411	0.594
sigma_H[5]	1.000	0.209	0.613	0.990	1.424
sigma_H[6]	0.389	0.204	0.029	0.383	0.808
sigma_H[7]	0.315	0.067	0.213	0.306	0.473
sigma_H[8]	0.417	0.089	0.276	0.407	0.606
sigma_H[9]	0.528	0.126	0.336	0.510	0.811
sigma_H[10]	0.216	0.043	0.141	0.213	0.310
sigma_H[11]	0.278	0.045	0.199	0.275	0.378
sigma_H[12]	0.438	0.168	0.212	0.408	0.785
sigma_H[13]	0.215	0.037	0.152	0.212	0.295
sigma_H[14]	0.513	0.096	0.347	0.506	0.713
sigma_H[15]	0.246	0.040	0.177	0.242	0.336
sigma_H[16]	0.227	0.043	0.154	0.221	0.328
lambda_H[1]	2.890	3.932	0.133	1.654	12.844
lambda_H[2]	8.044	7.558	0.817	5.819	27.450
lambda_H[3]	6.599	10.156	0.282	3.320	33.443
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	4.480	10.809	0.037	1.112	32.588
lambda_H[6]	6.893	13.056	0.008	0.897	44.752
lambda_H[7]	0.011	0.008	0.002	0.009	0.033
lambda_H[8]	8.400	10.400	0.131	4.927	37.891
lambda_H[9]	0.015	0.010	0.003	0.013	0.040
lambda_H[10]	0.324	0.634	0.035	0.211	1.122
lambda_H[11]	0.273	0.409	0.010	0.126	1.358
lambda_H[12]	4.989	6.549	0.223	2.912	22.173
lambda_H[13]	3.564	3.198	0.266	2.672	11.994
lambda_H[14]	3.455	4.250	0.224	2.108	14.742
lambda_H[15]	0.025	0.031	0.004	0.017	0.091
lambda_H[16]	0.789	1.100	0.038	0.430	3.737
mu_lambda_H[1]	4.369	1.869	1.271	4.183	8.339
mu_lambda_H[2]	3.883	1.950	0.618	3.752	8.072
mu_lambda_H[3]	3.559	1.870	0.798	3.267	7.774
sigma_lambda_H[1]	8.710	4.312	2.169	7.974	18.428
sigma_lambda_H[2]	8.497	4.683	1.049	7.997	18.509
sigma_lambda_H[3]	6.421	4.025	1.012	5.519	16.260
beta_H[1,1]	6.885	1.082	4.416	7.050	8.491
beta_H[2,1]	9.874	0.484	8.814	9.898	10.757
beta_H[3,1]	7.993	0.765	6.175	8.101	9.197
beta_H[4,1]	9.190	7.777	-7.342	9.381	24.242
beta_H[5,1]	0.204	2.430	-4.701	0.344	4.228
beta_H[6,1]	3.171	3.988	-6.711	4.647	7.822
beta_H[7,1]	-0.276	5.991	-13.247	0.053	10.503
beta_H[8,1]	1.387	3.817	-2.182	1.246	3.642
beta_H[9,1]	12.993	5.775	1.343	12.944	24.755
beta_H[10,1]	7.072	1.676	3.579	7.145	10.305
beta_H[11,1]	4.982	3.637	-3.334	5.688	9.947
beta_H[12,1]	2.639	1.018	0.868	2.560	4.959
beta_H[13,1]	9.036	0.954	7.132	9.118	10.491
beta_H[14,1]	2.190	1.002	0.247	2.206	4.156
beta_H[15,1]	-6.211	3.728	-12.869	-6.458	1.936
beta_H[16,1]	3.550	2.739	-0.729	3.158	10.036
beta_H[1,2]	7.904	0.245	7.405	7.911	8.363
beta_H[2,2]	10.029	0.135	9.756	10.029	10.290
beta_H[3,2]	8.947	0.191	8.570	8.948	9.326
beta_H[4,2]	3.612	1.481	0.924	3.551	6.660
beta_H[5,2]	1.972	0.952	0.070	2.008	3.760
beta_H[6,2]	5.734	1.068	3.283	5.897	7.415
beta_H[7,2]	2.911	1.145	0.875	2.836	5.330
beta_H[8,2]	3.007	1.076	1.446	3.151	4.270
beta_H[9,2]	3.500	1.121	1.432	3.466	5.824
beta_H[10,2]	8.211	0.338	7.514	8.229	8.850
beta_H[11,2]	9.789	0.658	8.820	9.662	11.253
beta_H[12,2]	3.950	0.370	3.265	3.939	4.750
beta_H[13,2]	9.119	0.260	8.665	9.107	9.634
beta_H[14,2]	4.023	0.351	3.341	4.018	4.750
beta_H[15,2]	11.374	0.675	9.900	11.425	12.594
beta_H[16,2]	4.535	0.815	3.016	4.510	6.198
beta_H[1,3]	8.474	0.239	8.046	8.459	8.981
beta_H[2,3]	10.068	0.118	9.845	10.066	10.308
beta_H[3,3]	9.614	0.162	9.308	9.608	9.951
beta_H[4,3]	-2.537	0.878	-4.246	-2.535	-0.850
beta_H[5,3]	3.822	0.615	2.603	3.839	5.022
beta_H[6,3]	8.013	1.197	6.346	7.649	10.574
beta_H[7,3]	-3.027	0.683	-4.444	-2.994	-1.733
beta_H[8,3]	5.249	0.497	4.651	5.181	6.206
beta_H[9,3]	-2.854	0.738	-4.307	-2.844	-1.451
beta_H[10,3]	8.679	0.270	8.154	8.681	9.215
beta_H[11,3]	8.532	0.294	7.890	8.560	9.031
beta_H[12,3]	5.259	0.312	4.502	5.301	5.752
beta_H[13,3]	8.836	0.174	8.486	8.840	9.175
beta_H[14,3]	5.721	0.283	5.107	5.737	6.213
beta_H[15,3]	10.359	0.306	9.795	10.352	10.966
beta_H[16,3]	6.224	0.603	4.919	6.282	7.211
beta_H[1,4]	8.260	0.180	7.867	8.274	8.576
beta_H[2,4]	10.128	0.121	9.884	10.134	10.349
beta_H[3,4]	10.123	0.162	9.765	10.139	10.407
beta_H[4,4]	11.799	0.449	10.893	11.804	12.671
beta_H[5,4]	5.447	0.744	4.267	5.352	7.122
beta_H[6,4]	7.041	0.919	4.980	7.323	8.322
beta_H[7,4]	8.316	0.362	7.563	8.318	8.983
beta_H[8,4]	6.701	0.252	6.245	6.713	7.134
beta_H[9,4]	7.200	0.468	6.286	7.202	8.111
beta_H[10,4]	7.758	0.235	7.325	7.750	8.270
beta_H[11,4]	9.391	0.202	9.002	9.386	9.796
beta_H[12,4]	7.143	0.207	6.748	7.142	7.585
beta_H[13,4]	9.046	0.140	8.761	9.047	9.317
beta_H[14,4]	7.732	0.217	7.305	7.735	8.163
beta_H[15,4]	9.471	0.233	9.018	9.475	9.909
beta_H[16,4]	9.352	0.244	8.913	9.341	9.859
beta_H[1,5]	8.978	0.143	8.695	8.982	9.250
beta_H[2,5]	10.783	0.096	10.604	10.780	10.985
beta_H[3,5]	10.914	0.175	10.611	10.905	11.282
beta_H[4,5]	8.385	0.459	7.492	8.373	9.321
beta_H[5,5]	5.412	0.581	4.082	5.453	6.427
beta_H[6,5]	8.792	0.627	7.891	8.648	10.269
beta_H[7,5]	6.732	0.353	6.061	6.732	7.436
beta_H[8,5]	8.214	0.211	7.855	8.203	8.631
beta_H[9,5]	8.228	0.480	7.306	8.232	9.193
beta_H[10,5]	10.079	0.229	9.620	10.078	10.529
beta_H[11,5]	11.510	0.232	11.046	11.508	11.975
beta_H[12,5]	8.484	0.196	8.098	8.477	8.881
beta_H[13,5]	10.007	0.129	9.755	10.006	10.265
beta_H[14,5]	9.196	0.233	8.775	9.189	9.684
beta_H[15,5]	11.162	0.250	10.677	11.160	11.661
beta_H[16,5]	9.916	0.184	9.536	9.919	10.263
beta_H[1,6]	10.189	0.194	9.847	10.179	10.638
beta_H[2,6]	11.513	0.108	11.292	11.513	11.723
beta_H[3,6]	10.815	0.161	10.466	10.824	11.098
beta_H[4,6]	12.882	0.797	11.299	12.894	14.439
beta_H[5,6]	5.911	0.597	4.774	5.890	7.133
beta_H[6,6]	8.751	0.669	6.963	8.868	9.747
beta_H[7,6]	9.905	0.593	8.753	9.917	11.094
beta_H[8,6]	9.515	0.281	9.011	9.526	9.968
beta_H[9,6]	8.460	0.794	6.832	8.472	10.015
beta_H[10,6]	9.516	0.315	8.855	9.531	10.081
beta_H[11,6]	10.812	0.356	10.035	10.833	11.444
beta_H[12,6]	9.379	0.252	8.922	9.362	9.923
beta_H[13,6]	11.047	0.162	10.755	11.038	11.381
beta_H[14,6]	9.832	0.295	9.263	9.832	10.411
beta_H[15,6]	10.840	0.439	9.964	10.852	11.667
beta_H[16,6]	10.539	0.243	10.033	10.547	11.001
beta_H[1,7]	10.872	0.869	8.800	11.001	12.264
beta_H[2,7]	12.202	0.433	11.290	12.212	13.003
beta_H[3,7]	10.580	0.666	9.051	10.643	11.714
beta_H[4,7]	2.534	4.086	-5.125	2.519	10.640
beta_H[5,7]	6.427	1.900	3.095	6.392	10.542
beta_H[6,7]	9.582	2.480	5.003	9.501	16.266
beta_H[7,7]	10.371	2.972	4.440	10.325	16.101
beta_H[8,7]	10.980	1.035	9.522	10.925	12.634
beta_H[9,7]	4.423	4.078	-3.700	4.488	12.306
beta_H[10,7]	9.816	1.442	7.207	9.729	12.897
beta_H[11,7]	11.026	1.707	7.917	10.900	14.784
beta_H[12,7]	10.026	0.886	8.115	10.085	11.558
beta_H[13,7]	11.664	0.774	9.835	11.767	12.860
beta_H[14,7]	10.407	0.955	8.373	10.470	12.170
beta_H[15,7]	12.016	2.257	7.687	11.983	16.596
beta_H[16,7]	12.289	1.284	10.201	12.141	15.124
beta0_H[1]	8.853	13.616	-18.338	9.014	36.069
beta0_H[2]	10.625	6.289	-1.633	10.485	23.457
beta0_H[3]	10.019	9.581	-9.618	9.976	29.417
beta0_H[4]	1.665	179.160	-367.006	3.303	352.641
beta0_H[5]	3.815	25.462	-46.022	4.149	48.283
beta0_H[6]	6.970	50.294	-105.890	7.609	115.790
beta0_H[7]	4.505	146.897	-290.620	1.077	310.828
beta0_H[8]	5.666	32.561	-15.980	6.468	27.600
beta0_H[9]	8.921	121.863	-237.352	9.559	265.684
beta0_H[10]	9.927	32.561	-52.511	8.958	78.195
beta0_H[11]	10.026	50.524	-93.785	9.211	118.643
beta0_H[12]	6.660	11.049	-15.346	6.620	28.688
beta0_H[13]	9.500	10.922	-12.354	9.682	30.523
beta0_H[14]	7.157	11.325	-14.854	7.052	28.899
beta0_H[15]	7.266	108.921	-214.261	7.938	231.876
beta0_H[16]	8.381	25.770	-42.468	8.357	62.910